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• Introduction-- Part I. Geometric Constructions:
• 1. Examples and basic folds--
• 2. Solving equations via folding--
• 3. Origami algebra--
• 4. Beyond classic origami-- Part II. The Combinatorial Geometry of Flat Origami:
• 5. Flat vertex folds: local properties--
• 6. Multiple-vertex flat folds: global properties--
• 7. Counting flat folds--
• 8. Other flat folding problems-- Part III. Algebra, Topology, and Analysis in Origami:
• 9. Origami homomorphisms--
• 10. Folding manifolds--
• 11. An analytic approach to isometric foldings-- Part IV. Non-Flat Folding:
• 12. Rigid origami--
• 13. Rigid foldings--
• 14. Rigid origami theory-- References-- Index.
• (source: Nielsen Book Data)

Origami, the art of paper folding, has a rich mathematical theory. Early investigations go back to at least the 1930s, but the twenty-first century has seen a remarkable blossoming of the mathematics of folding. Besides its use in describing origami and designing new models, it is also finding real-world applications from building nano-scale robots to deploying large solar arrays in space. Written by a world expert on the subject, Origametry is the first complete reference on the mathematics of origami. It brings together historical results, modern developments, and future directions into a cohesive whole. Over 180 figures illustrate the constructions described while numerous 'diversions' provide jumping-off points for readers to deepen their understanding. This book is an essential reference for researchers of origami mathematics and its applications in physics, engineering, and design. Educators, students, and enthusiasts will also find much to enjoy in this fascinating account of the mathematics of folding.
(source: Nielsen Book Data)

• Table of Contents Introduction Building Blocks Elephant Design Traditional Bases Folding Instructions Stealth Fighter. Snail. Valentine. Ruby-Throated Hummingbird. Baby. Splitting Points Folding Instructions Pteranodon. Goatfish. Grafting Folding Instructions Songbird
• 1. KNL Dragon. Lizard. Tree Frog. Dancing Crane. Pattern Grafting Folding Instructions Turtle. Western Pond Turtle. Koi. Tiling Folding Instructions Pegasus Circle Packing Folding Instructions Emu. Songbird
• 2. Molecules Folding Instructions Orchid Blossom. Silverfish. Tree Theory Folding Instructions Alamo Stallion. Roosevelt Elk. Box Pleating Folding Instructions Organist. Black Forest Cuckoo Clock. Uniaxial Box Pleating Folding Instructions Bull Moose Polygon Packing Crease Patterns Flying Walking Stick. Salt Creek Tiger Beetle. Longhorn Beetle. Camel Spider. Water Strider. Scarab Beetle. Cicada Nymph. Scarab HP. Cyclomatus metallifer. Scorpion HP. Euthysanius Beetle. Spur-Legged Dung Beetle. Hybrid Bases Folding Instructions African Elephant References Glossary of Terms Index.
• (source: Nielsen Book Data)

The magnum opus of one of the world's leading origami artists, the second edition of Origami Design Secrets reveals the underlying concepts of origami and how to create original origami designs. Containing step-by-step instructions for 26 models, this book is not just an origami cookbook or list of instructions-it introduces the fundamental building blocks of origami, building up to advanced methods such as the combination of uniaxial bases, the circle/river method, and tree theory. With corrections and improved illustrations, this new expanded edition also covers uniaxial box pleating, introduces the new design technique of hex pleating, and describes methods of generalizing polygon packing to arbitrary angles. With coverage spanning the foundations of origami construction and advanced methods using both paper and pencil and custom-built free software, Origami Design Secrets helps readers cultivate the intuition and skills necessary to develop their own designs. It takes them beyond merely following a recipe to crafting a work of art.
(source: Nielsen Book Data)

Robert J. Lang, one of the worlds foremost origami artists and scientists, presents the never-before-described mathematical and geometric principles that allow anyone to design original origami, something once restricted to an elite few. From the theoretical underpinnings to detailed step-by-step folding sequences, this book takes a modern look at the centuries-old art of origami.
(source: Nielsen Book Data)

• Introduction to origami.- Origami geometry and basic folds.- Algebra of folds.- Origami geometry vs. Euclid geometry.- Examples.- Origami theorems and verification.- Extensions of basic folds.- Three-dimensional origami.
• (source: Nielsen Book Data)

In this book, origami is treated as a set of basic geometrical objects that are represented and manipulated symbolically and graphically by computers. Focusing on how classical and modern geometrical problems are solved by means of origami, the book explains the methods not only with mathematical rigor but also by appealing to our scientific intuition, combining mathematical formulas and graphical images to do so. In turn, it discusses the verification of origami using computer software and symbolic computation tools. The binary code for the origami software, called Eos and created by the author, is also provided.
(source: Nielsen Book Data)

• 1. Origami history, art, and design
• 2. Origami in education
• 3. Origami science, engineering, and technology
• 4. Mathematics of origami.

Origami5 continues in the excellent tradition of its four previous incarnations, documenting work presented at an extraordinary series of meetings that explored the connections between origami, mathematics, science, technology, education, and other academic fields. The fifth such meeting, 5OSME (July 13-17, 2010, Singapore Management University) followed the precedent previous meetings to explore the interdisciplinary connections between origami and the real world. This book begins with a section on origami history, art, and design. It is followed by sections on origami in education and origami science, engineering, and technology, and culminates with a section on origami mathematics-the pairing that inspired the original meeting. Within this one volume, you will find a broad selection of historical information, artists' descriptions of their processes, various perspectives and approaches to the use of origami in education, mathematical tools for origami design, applications of folding in engineering and technology, as well as original and cutting-edge research on the mathematical underpinnings of origami.
(source: Nielsen Book Data)

This title contains select contributions from the Fourth International Conference on Origami in Science, Mathematics, and Education (4OSME), held September 8-10, 2006, in Pasadena, CA (sponsored by OrigamiUSA, in collaboration with the California Institute of Technology). The conference has been held approximately once every five years (since the first one in 1989), and it focuses on the mathematics of origami and applications of origami in the sciences.
(source: Nielsen Book Data)

• pt.
• 1. Mathematics of origami
• pt.
• 2. Origami science and applications
• pt.
• 3. Origami in education

The book contains papers from the proceedings of the 3rd International Meeting of Origami Science, Math, and Education, sponsored by OrigamiUSA. They cover topics ranging from the mathematics of origami using polygon constructions and geometric projections, applications, and science of origami, and the use of origami in education.
(source: Nielsen Book Data)

• * Mathematics of origami: Coloring: Coloring connections with counting mountain-valley assignments by T. C. Hull* Color symmetry approach to the construction of crystallographic flat origami by M. L. A. de las Penas, E. C. Taganap, and T. A. Rapanut* Symmetric colorings of polypolyhedra by S.-H. Belcastro and T. C. Hull* Mathematics of origami: constructibility: Geometric and arithmetic relations concerning origami by J. Guardia and E. Tramuns* Abelian and non-abelian numbers via 3D origami by J. I. Royo Prieto and E. Tramuns* Interactive construction and automated proof in Eos system with application to knot fold of regular polygons by F. Ghourabi, T. Ida, and K. Takahashi* Equal division on any polygon side by folding by S. Chen* A survey and recent results about commmon developments of two or more boxes by R. Uehara* Unfolding simple folds from crease patterns by H. A. Akitaya, Y. Kanamori, Y. Fukui, and J. Mitani* Mathematics of origami: Rigid foldability: Rigid folding of periodic origami tessellations by T. Tachi* Rigid flattening of polyhedra with slits by Z. Abel, R. Connelly, E. Demaine, M. L. Demaine, T. C. Hull, A. Lubiw, and T. Tachi* Rigidly foldable origami twists by T. A. Evans, R. J. Lang, S. P. Magleby, and L. L. Howell* Locked rigid origami with multiple degrees of freedom by Z. Abel, T. C. Hull, and T. Tachi* Screw-algebra-based kinematic and static modeling of origami-inspired mechanisms by K. Zhang, C. Qiu, and J. S. Dai* Thick rigidly foldable structures realized by an offset panel technique by B. J. Edmondson, R. J. Lang, M. R. Morgan, S. P. Magleby, and L. L. Howell* Configuration transformation and manipulation of origami cartons by J. S. Dai* Mathematics of origami: design algorithms: Filling a hole in a crease pattern: Isometric mapping from prescribed boundary folding by E. D. Demaine and J. S. Ku* Spiderwebs, tilings, and flagstone tessellations by R. J. Lang* Scaling any surface down to any fraction by E. D. Demaine, M. L. Demaine, and K. Qaiser* Characterization of curved creases and rulings: Design and analysis of lens tessellations by E. D. Demaine, M. L. Demaine, D. A. Huffmann, D. Koschitz, and T. Tachi* Curve-folding polyhedra skeletons through smoothing by S. Chandra, S. Bhooshan, and M. El-Sayed* Design methods of origami tessellations for triangular spiral multiple tilings by T. Sushida, A. Huzume, and Y. Yamagishi* A new scheme to describe twist-fold tessellations by T. R. Crain* Weaving a uniformly thick sheet from rectangles by E. Davis, E. D. Demaine, M. L. Demaine, and J. Ramseyer* Extruding towers by serially grafting prismoids by H. Y. Cheng* On pleat rearrangements in pureland tessellations by G. Konjevod* Graph paper for polygon-packed origami design by R. J. Lang and R. C. Alperin* A method to fold generalized bird bases from a given quadrilateral containing an inscribed circle by T. Kawasaki* Pentasia: An aperiodic origami surface by R. J. Lang and B. Hayes* Base design of a snowflake curve model and its difficulties by U. Ikegami* Two calculations for geodesic modular works by M. Kawamura* Index.
• (source: Nielsen Book Data)

• * Mathematics of origami: Comparison of compressive properties of periodic non-flat tessellations by Y. Klett, M. Grzeschik, and P. Middenhorf* Numerical analysis of origami structures through modified frame elements by K. Fuchi, P. R. Buskohl, J. J. Joo, G. W. Reich, and R. A. Vaia* A study on crash energy absorption ability of lightweight structures with truss core panel by Y. Yang, X. Zhao, S. Tokura, and I. Hagiwara* Toward optimization of stiffness and flexibility of rigid, flat-foldable origami structures by E. T. Filipov, T. Tachi, and G. H. Paulino* Structural engineering applications of morphing sandwich structures by J. M. Gattas and Z. You* Sound-insulting performance of origami-based sandwich trusscore panels by S. Ishida, H. Morimura, and I. Hagiwara* Thin-walled deployable grid structures by J. Ho and Z. You* Deployable linear folded stripe structures by R. Maleczek* Gravity and friction-driven self-organized folding by G. H. Filz, G. Grasser, J. Ladinig, and R. Maleczek* Magnetic self-assembly of three-dimensional microstructures by E. Iwase and I. Shimoyama* Folding augmented: A design method to integrate structural folding in archietecture by P. D'Acunto and J. J. C. Castellon Gonzalez* Demands on an adapted design process for foldable structures by S. Hoffmann, M. Barej, B. Gunther, M. Trautz, B. Corves, and J. Feldhusen* Planning motions for shape-memory alloy sheets by M. Ghosh, D. Tomkins, J. Denny, S. Rodriguez, M. Morales, and N. M. Amato* Simple flat origami exploration system with random folds by N. Tsuruta, J. Mitani, Y. Kanamori, and Y. Fukui* ORICREATE: Modeling framework for design and manufacturing of folded plate structures by R. Chudoba, J. van der Woerd, and J. Hegger* Rotation erection system (res): Origami extended with cuts by Y. Miyamoto* Toward engineering biological tissues by directed assembly and origami folding by P. J. Mehner, T. Liu, A. B. Karimi, A. Brodeur, J. Paniagua, S. Giles, P. Richard, A. Nemtserova, S. Liu, R. C. Alperin, S. Bhatia, M. Culpepper, R. J. Lang, and C. Livermore* Cosmological origami: Properties of cosmic-web components when a non-stretchy dark-matter sheet folds by M. C. Neyrinck* Modeling vaults in origami: A bridge between mathematics and architecture by C. Cumino, E. Frigerio, S. Gallina, M. L. Spreafico, and U. Zich* Origami in art, design, and history: Folding perspectives: Joys and uses of 3d anomorhic origami by Y. Klett* Master peace: An evolution of monumental origami by K. Box and R. J. Lang* Wearable metal origami by T. de Ruysser* Crowdsourcing origami sculptures by J. Mosely* On the aesthetics of folding and technology: Scale, dimensionality, and materiality by M. Gardiner* Computational problems related to paper crane in the Edo period by J. Maekawa* Mitate and origami by H. Koshiro* Origami in education: The kindergarten origametria programme by M. Golan and J. Oberman* Area and optimization problems by E. Frigerio and M. L. Spreafico* Mathematics and art through the cubotahedron by S.-P. Kwan* Origami-inspired deductive threads in pre-geometry by A. Tubis* Using paper folding to solve problems in school geometry by H. Yanping and P.-Y. Lee* Using origami to enrich mathematical understanding of self similarity and fractals by A. Bahmani, K. Sharif, and A. Hudson* Using the Fujimoto approximation technique to teach chaos theory to high school students by L. Poladian* Index.
• (source: Nielsen Book Data)

A unique collection of papers illustrating the connections between origami and a wide range of fields. The papers compiled in this two-part set were presented at the 6th International Meeting on Origami in Science, Mathematics and Education (10-13 August 2014, Tokyo, Japan). They display the creative melding of origami (or, more broadly, folding) with fields ranging from cell biology to space exploration, from education to kinematics, from abstract mathematical laws to the artistic and aesthetics of sculptural design. This two-part book contains papers accessible to a wide audience, including those interested in art, design, history, and education and researchers interested in the connections between origami and science, technology, engineering, and mathematics. This Part 1 contains papers on various aspects of mathematics of origami: coloring, constructability, rigid foldability, and design algorithms.
(source: Nielsen Book Data)

• Part I. Linkages:
• 1. Robot arms--
• 2. Straight-line linkages and the pantograph--
• 3. Protein folding and pop-up cards-- Part II. Origami:
• 4. Flat vertex folds--
• 5. Fold and one-cut--
• 6. The shopping bag theorem-- Part III. Polyhedra:
• 7. Durer's problem: edge unfolding--
• 8. Unfolding orthogonal polyhedra--
• 9. Folding polygons to convex polyhedra--
• 10. Further reading--
• 11. Glossary--
• 12. Answers to exercises--
• 13. Permissions and acknowledgments.
• (source: Nielsen Book Data)

What do proteins and pop-up cards have in common? How is opening a grocery bag different from opening a gift box? How can you cut out the letters for a whole word all at once with one straight scissors cut? How many ways are there to flatten a cube? With the help of 200 colour figures, author Joseph O'Rourke explains these fascinating folding problems starting from high school algebra and geometry and introducing more advanced concepts in tangible contexts as they arise. He shows how variations on these basic problems lead directly to the frontiers of current mathematical research and offers ten accessible unsolved problems for the enterprising reader. Before tackling these, you can test your skills on fifty exercises with complete solutions. The book's website, http://www.howtofoldit.org, has dynamic animations of many of the foldings and downloadable templates for readers to fold or cut out.
(source: Nielsen Book Data)

• pt.
• 1. Mathematics of origami
• pt.
• 2. Origami science and applications
• pt.
• 3. Origami in education.

The book contains papers from the proceedings of the 3rd International Meeting of Origami Science, Math, and Education, sponsored by OrigamiUSA. They cover topics ranging from the mathematics of origami using polygon constructions and geometric projections, applications, and science of origami, and the use of origami in education.
(source: Nielsen Book Data)

• Introduction Activity 1 Folding Equilateral Triangles in a Square Activity 2 Origami Trigonometry Activity 3 Dividing a Length into Equal Nths: Fujimoto Approximation Activity 4 Dividing a Length into Equal Nths Exactly Activity 5 Origami Helix Activity 6 Folding a Parabola Activity 7 Can Origami Trisect an Angle? Activity 8 Solving Cubic Equations Activity 9 Lill's Method Activity 10 Folding Strips into Knots Activity 11 Haga's "Origamics" Activity 12 Modular Star Ring Activity 13 Folding a Butterfly Bomb Activity 14 Molly's Hexahedron Activity 15 Business Card Modulars Activity 16 Five Intersecting Tetrahedra Activity 17 Making Origami Buckyballs Activity 18 Making Origami Tori Activity 19 Modular Menger Sponge Activity 20 Folding and Coloring a Crane Activity 21 Exploring Flat Vertex Folds Activity 22 Impossible Crease Patterns Activity 23 Folding a Square Twist Activity 24 Counting Flat Folds Activity 25 Self-Similar Wave Activity 26 Matrix Model of Flat Vertex Folds Activity 27 Matrix Model of 3D Vertex Folds Activity 28 Origami and Homomorphisms Activity 29 Rigid Folds
• 1: Gaussian Curvature Activity 30 Rigid Folds
• 2: Spherical Trigonometry Appendix: Which Activities Go with Which Courses Bibliography Index.
• (source: Nielsen Book Data)

Project Origami: Activities for Exploring Mathematics, Second Edition presents a flexible, discovery-based approach to learning origami-math topics. It helps readers see how origami intersects a variety of mathematical topics, from the more obvious realm of geometry to the fields of algebra, number theory, and combinatorics. With over 100 new pages, this updated and expanded edition now includes 30 activities and offers better solutions and teaching tips for all activities. The book contains detailed plans for 30 hands-on, scalable origami activities. Each activity lists courses in which the activity might fit, includes handouts for classroom use, and provides notes for instructors on solutions, how the handouts can be used, and other pedagogical suggestions. The handouts are also available on the book's CRC Press web page. Reflecting feedback from teachers and students who have used the book, this classroom-tested text provides an easy and entertaining way for teachers to incorporate origami into a range of college and advanced high school math courses. Visit the author's website for more information.
(source: Nielsen Book Data)

• Part I. Linkages:
• 1. Robot arms--
• 2. Straight-line linkages and the pantograph--
• 3. Protein folding and pop-up cards-- Part II. Origami:
• 4. Flat vertex folds--
• 5. Fold and one-cut--
• 6. The shopping bag theorem-- Part III. Polyhedra:
• 7. Durer's problem: edge unfolding--
• 8. Unfolding orthogonal polyhedra--
• 9. Folding polygons to convex polyhedra--
• 10. Further reading--
• 11. Glossary--
• 12. Answers to exercises--
• 13. Permissions and acknowledgments.
• (source: Nielsen Book Data)

What do proteins and pop-up cards have in common? How is opening a grocery bag different from opening a gift box? How can you cut out the letters for a whole word all at once with one straight scissors cut? How many ways are there to flatten a cube? With the help of 200 colour figures, author Joseph O'Rourke explains these fascinating folding problems starting from high school algebra and geometry and introducing more advanced concepts in tangible contexts as they arise. He shows how variations on these basic problems lead directly to the frontiers of current mathematical research and offers ten accessible unsolved problems for the enterprising reader. Before tackling these, you can test your skills on fifty exercises with complete solutions. The book's website, http://www.howtofoldit.org, has dynamic animations of many of the foldings and downloadable templates for readers to fold or cut out.
(source: Nielsen Book Data)